Tax efficiency - selected ishares, Vanguard, and DFA funds

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Robert T
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Tax efficiency - selected ishares, Vanguard, and DFA funds

Post by Robert T » Thu Oct 11, 2007 9:46 pm

.
Just reviewed the tax-efficiency of most of the funds I use as its now about 5 years of IPS implementation. I thought it may be useful to share the results and have also added the tax efficiency of several DFA funds for comparison (as a benchmark). Here are some observations (see table below):

1. It was interesting that some of the most tax efficient funds over the last 5 years have been in asset classes often viewed as tax-inefficient. The Bridgeway ultra-small company market fund and ishare S&P600 small value were the most tax efficient, while US TSM and TM Intl large cap came down the list. Perhaps just a last five-year phenomena?

2. The absolute tax costs of the funds used range from 0.19 to 0.38% compared to the DFA funds, which range from 0.17 to 1.12% in absolute terms. Four of the six funds were more tax-efficient than a DFA ‘comparison/benchmark’ (exceptions were DFA TM Mkt-wide and EM although not by much).

3. Turnover of the S&P400 and 600 indexes over the last 5 years has been almost half the levels of that in yr 6-10 (see second table below), some of the funds listed may not be as tax efficient going forward if index turnover increases to earlier levels.

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Five year tax efficiency to December 2006

                                              
US LARGE MARKET                  Vanguard TSM        DFA US Large
Before Tax                           7.42                6.06
After Tax                            7.10	             5.70
Difference                           0.32                0.64
% of return lost to taxes            4.31               10.56	 

US LARGE VALUE                   iShares 400v      DFA US TM Mkt-Wide
Before tax                          13.63                9.67
After Tax                           13.25                9.50
Difference                           0.38                0.17
% of return lost to taxes            2.79                1.76

US MICRO MARKET                Bridgeway[BRSIX]*       DFA Micro
Before Tax                          23.88               15.16     
After Tax                           23.69               14.04
Difference                           0.19                1.12
% of return lost to taxes            0.78 	            7.39 

US SMALL VALUE                  iShares 600v       DFA TM Trgtd Value
Before Tax                          13.13               14.81	
After Tax                           12.88               14.08
Difference                           0.25                0.73  
% of return lost to taxes            1.90                4.93
                                                       
INTL. LARGE MARKET             Vgd Tax-Mgd Intl      DFA Intl. Large
Before Tax                          15.08               14.46
After Tax                           14.75               14.02
Difference                           0.33                0.44 
% of return lost to taxes            2.19                3.04

EMERGING MARKET                    Vgd EM              DFA EM
Before Tax                          25.51               25.74
After Tax                           25.17               25.49
Difference                           0.33                0.25
Percent of return lost to taxes      1.29                0.97

* Uses 5 yr ending 2005 (latest prospectus)
Source: ishares, Vanguard, Bridgeway and DFA prospectus.

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INDEX TURNOVER

        S&P 500   S&P MidCap 400   S&P SmallCap 600*
1995     5.0%         15.6%             13.7%
1996     4.6%         14.4%             16.4%
1997     4.9%         17.9%             21.8%
1998     9.5%         31.4%             24.4%
1999     6.2%         28.9%             24.4%
2000     8.9%         37.1%             36.4%
2001     4.4%         17.0%             15.6%
2002     3.8%         10.7%             11.0%
2003     1.5%          8.6%             11.0%
2004     3.1%         13.1%             13.0%
2005     5.7%         14.5%             13.8%
2006     4.5%         12.2%             12.9%

Source: S&P website
So at least so far I have managed to acheive my risk tilts (factor loadings) in a reasonably tax-efficient way (better than expected).

Robert
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Post by SmallHi » Thu Oct 11, 2007 10:22 pm

Robert,

Nice work! I think you are displaying a bit of "index selection alpha"! :D

I happened to be looking at the same thing this weekend using a slightly different set of indicies, and came to the disturbing conclusion that, outside of US Large Market, the after fee, after tax returns of common DFA funds were between 1% and 7% ahead of their comparable index on a gross of fee, pretax basis.

10/02-9/07
(DFA Funds = net of fee, after tax returns; Index = gross of fee, pre tax)

TM US Market = +15.1%
Russell 3000 = +16.2%

TM US Marketwide Value = +19.1%
Russell 3000 Value = +18.1%

TM US Small Cap = +19.9%
Russell 2000 = +18.8%

TM US Targeted Value = +20.0%
Russell 2000 Value = +18.7%

TM Int'l Large Value = +27.9%
MSCI EAFE Value = +25.7%

Int'l Small Value = +31.1%
EAFE Small Cap Index = +28.0%

Emerging Markets Value = +45.9%
MSCI EM Index = +39.1%

DFA Portfolio = +24.4% (net of fee, after tax)
Index Portfolio = +22.7% (gross of fee, pre tax)

allocations = 20% US Large, US Large Value, 10% US Small, US Small Value, 15% Int'l Large Value, 15% Int'l Small Value, 10% Emerging Markets

Incidentially, a non-tax managed DFA fund portfolio with identical weightings would have underperformed the tax-managed version by about 0.3% annually for the last 5 years. Less that I understood the 0.5% to 0.75% goal to be.

I looked at the AT returns of all DFA funds in the Large, Small, Market and Value asset classes in the US, Int'l, and EM asset classes over the last 5 years. Each Value, Small, and Small Value fund had significant outperformance, and each "market" portfolio underperformed its relevant index when using the Russell/MSCI indexes I chose.

The moral of the story maybe, indexing global beta may still be the way to go for taxable investors!

SH

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Slice and Dice / Value Tilting for Taxable

Post by barkster » Fri Oct 12, 2007 1:44 am

Thanks for the info. I often see opinions against slicing and dicing as well as value tilting for taxable accounts.

DFA recently posted the following on their site:

"The US Small Cap Value Portfolio II made a special distribution of $8.456 on Thursday, September 27 representing approximately 30% of its net asset value. This action did not decrease the fund's account value and does not negatively impact the fund's return. The fund's net asset value was reduced by the amount of the distribution, which will be reinvested into additional shares of the fund for all shareholders who chose to reinvest distributions."

Why would they make such a large distribution? That would really hurt a taxable investor who invested recently in that fund. Could this happen to some of the non tax managed funds you listed above like International Small Value and Emerging Markets Value?

They also seem to have launched the U.S. Tax Aware Core 2 fund. Hopefully the EM+Intl version that Larry Swedroe mentioned will be available soon as well.

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Post by Robert T » Fri Oct 12, 2007 3:33 am

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SH,

Thanks for the numbers.

I expect that some of the differences in return is due to differences in factor exposure across the funds. A more direct comparison may be between the returns of portfolios with the same factor loadings. As you know one of the main advantages of DFA funds is that many (most) of their small cap and value funds have higher factor loadings than the corresponding asset class index funds so a smaller allocation is needed to reach a particular laoding target. Given a large share would then be allocated to a more ‘tax-efficient’ asset class (e.g. large market) the overall sum has a good chance of being more tax efficient. What some of the data above highlighted was that the difference in tax efficiency across funds is relatively small so having to add a larger share of small value or small cap stocks did not (at least over the 5 years) create a tax disadvantage for a non-DFA portfolio (not sure if I explained this too well).

barkster,

Here are the annualized return numbers for DFA targeted value and small cap value (five years to Dec. 2006)

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DFA US Targeted Value
Return before taxes            17.81   
Return after taxes             15.15
Difference                      2.66
% return lost to taxes         14.94

DFA US Small Cap Value
Return before taxes            18.90
Return after taxes             17.15 
Difference                      1.75
% return lost to taxes          9.26
The after tax returns for US targeted value was still larger than the after tax return of its tax-managed counterpart (15.15 vs. 14.08.), but would expected there to be a slight difference in factor loadings between the funds. IMO if someone wants to use DFA funds in a taxable account then the tax-managed or tax-aware funds are a better option than their non-tax managed counterparts.

Robert
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Post by SmallHi » Fri Oct 12, 2007 12:36 pm

Barkster,

That fund is a version that is only used by institutions and pensions I believe (its assets are less than 1/10 that of Small Value I). I have to believe that is a special case where one institution may have yanked money from the fund unexpectedly (200M or so?) causing that distribution. I doubt that will have an impact on DFSVX, but who knows?

Robert,

I agree with your thoughts. Also, your data is about 9 months old, and DFAs TM funds did have some severe tracking error in 2002 which drags down their performance considerably--and causes large differences in actual results. That was not (I understand) supposed to be an ongoing issue, and in fact it hasn't been. Of the 4 TM funds DFA runs on the US side, only TM Small Value has underperformed DFSVX on an after tax basis for the 5 years ended 9/07, and that was only by 0.3% annually.

Its really hard to make an apples to apples comparison for the sheer fact that, ideally, you don't want a lot of Int'l and Emerging Markets "market exposure". Where you seem to have taken a lot of the 3F risk in the US market, for diversification purposes, I may argue, longer term, it is preferable to do so in the Int'l markets. Int'l tracking error isn't a huge problem for most, and you get better diversification that way. As I believe you have done in your 529 plan.

Over the last 5 years, if you factor/adjust the Russell & DFA portfolios to maintain a constant factor exposure, you come up with the following changes (I used factor exposures since 1979 for more dependability)

33% Russell 3000, Russell 3000 Value; 17% Russell 2000, Russell 2000 Value

=

40% DFA TM Market; 35% DFA TM Marketwide Value; 15% DFA TM Small Cap; 10% DFA TM Targeted Value


Since 10/02, the pretax, gross of fee Russell returns have been 17.7% a year, and the after tax, net of fee returns for DFA have been 17.6%.

The Core Equity version of this portfolio would be 85% US Core 2, 15% Marketwide Value. If we assume the after fee, aftertax return of DFQTX since 2002 would be about 1.0% less per year than the Core 2 Simulated Index...the 85% US Core 2, 15% Tax-Managed Marketwide Value fund net of fee, after tax performance would have been about 18.0%. Over this period, no rebalancing would have been necessary between the two holdings, unlike the Russell or DFA component fund portfolio.

Finally, its even trickier to factor adjust Int'l portfolios. An EAFE Value index is similar to a 40% DFA Int'l Large, 60% DFA TM Int'l Value portfolio, which, over the last 5 years has after fee, after tax performance that has matched the pretax, gross of fee performance of EAFE Value. EAFE Small is similar to DFA Int'l Small in factor exposure, and DFA ISC has outpaced EAFE Small on a net fee/after tax basis by about 0.4% a year since 9/02.

I guess you must ignore DFA Int'l SV, as it is unachievable (factor wise) with ETFs.

As for EM Markets, I hesitate to compare MSCI EM Index to DFA EM Markets, because you are completely ignoring EM Value and EM Small. So, at best, outside of the developed world, you start to get into a grey area.

Thanks for the analysis, by the way.

SH

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The disappearance of "SmallHi"?

Post by SmallHi » Fri Oct 12, 2007 1:00 pm

Robert,

Another comment I might add (that is not related to the discussion above), is that, with the US, and Int'l Core Equity funds from DFA, theoretically for many (most?) reasonable tilts to small and value (say 0.3 SmB or less, and 0.35 HmL or less), a dedicated SV fund -- DFA US SV, Targed Value, S&P 600 Value, or Russell 2000 Value really isn't necessary....its the "disappearence of SmallHi", if you will! :D

I would consider a pretty agressive tilt to size/value using Russell to be something along the lines of 30% R3K, R3K VL; 20% R2K, R2K VL, or even something like 4X25 of the above mix.

Each "target" can be hit with DFA funds by maintaining 65% to 75% in the Core portfolio, adding just a bit of Marketwide Value, and a pinch of Small Market.

For the 3F junkie, you really can get to most extreme 0.4 to 0.55 tilts using mostly Vector.

On the Int'l side, 50% EAFE Value and 50% EAFE Small (my preference for ETF foreign exposure) really gets you to about the same place as the DFA Int'l Core Equity fund...without any need for Int'l Value, Int'l Small or Int'l Small Value.

For Emerging Markets, DFA EM Core is going to be very similar to the "as of yet to be released" MSCI EM Small Index and the MSCI EM Value index (again, in 50/50 allocations) in terms of factor exposure.

While these Core funds may be "watered down or weak" in terms of DFAs more concentrated component funds, they are very close to retail small/value index ETFs combo's in terms of factor exposure -- which is probably preferable to all but diehard FF 3F investors to begin with...

SH

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Core benefits

Post by Robert T » Fri Oct 12, 2007 6:56 pm

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Since 10/02, the pretax, gross of fee Russell returns have been 17.7% a year, and the after tax, net of fee returns for DFA have been 17.6%.
Thanks for the portfolio comparison (with similar factor tilts across the two portfolios). As anticipated the results are much closer (the DFA portfolio is also gross the advisor fee ...:))

I am still trying to understand the comparison made with the core strategies (or rather the advantages of the core approach). The stated advantages are:

1. Lower capital gains distributions: A core equity approach may lower capital gains distributions compared to open ended mutual funds but it’s not clear that it lowers capital gains distributions compared to an ETF structure (assuming no rebalancing). But even with rebalancing – its often more frequent between US, non-US developed, EM, and bonds than within each of these groups and there is less scope for tax-loss harvesting opportunities. So not sure what the actual magnitude of the capital gains benefit will be?

2. Lower transaction costs: A core equity approach may lower commissions, bid-ask spreads and market impact (lower turnover in high cap stocks leading to lower transaction costs). However I am not sure how large this effect is given many component index funds currently stick fairly close to their underlying index (for example the 5 year annualized return to 9/30/07 of the S&P600v index is 18.41% while the corresponding ishares fund return was 18.13% for a difference of 0.28% subtract from this the expense ratio of 0.25% and we are left with 0.03%). The micro-cap asset class seems to be the exception in this respect.

The core approach also assumes linearity in risk premiums. However market cap decile data indicate some non-linearity (highest premiums for micro-cap stocks) so not sure what is lost by shifting from micro-cap to a mid-cap exposure (to acheive the same portfolio factor loadings). I have not yet had time to look at the magnitude of this effect.

Still trying to fully understand these products.

Robert
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Previous realized losses

Post by grabiner » Fri Oct 12, 2007 11:24 pm

Robert T wrote:
1. It was interesting that some of the most tax efficient funds over the last 5 years have been in asset classes often viewed as tax-inefficient. The Bridgeway ultra-small company market fund and ishare S&P600 small value were the most tax efficient, while US TSM and TM Intl large cap came down the list. Perhaps just a last five-year phenomena?
None of the funds realized capital gains, so what you are seeing is the effect of the dividend yield. The Bridgeway ultra-small company market funds has the lowest dividend yield, partly because it has the highest expenses of any of the indexes, and partly because micro-caps are less likely to pay dividends.

Bridgeway's fund is tax-managed and may be able to avoid realizing gains, but I wouldn't expect small-value funds to be able to avoid gains forever. The small-cap value index realized a lot of losses in 2000-2002 and has been able to offset its gains with those losses.

And actually, the lowest tax cost of all is DFA Emerging Markets Index, with Vanguard second (and probably only second because it has lower costs and thus more taxable dividends). The foreign tax credit is worth about 0.24%, and you lose it in a tax-deferred account, so the DFA index actually has a tax cost of zero (equal returns in taxable and tax-deferred!) and Vanguard's is 0.09%.

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Post by SmallHi » Sat Oct 13, 2007 9:16 am

Robert, I just wanted to throw out some random thoughts regarding the Core funds I have read/considered -- many of which you are already familiar with:

a) Core's have constant risk factor exposure because they are rebalanced daily with new cashflows. It maybe hard to quantify what this actually "adds", but this is clearly preferable to 1 day per year targeted exposure. Its not uncommon to see index funds with factor exposures that are 7-10% less than their average if you isolate the 6-9 months after reconstitution.

b) almost no selling takes place in the smaller/value regions of the market. some of this etf "drawback" shows up in the lower gross returns of the index, not in the etf to index comparison. (the impact on stock prices when the S&P 600 Value ETF or index fund buys newly included stocks or sells deleted names per reconstitution is on the index and the fund equally -- because they are added/deleted at the same time). theoretically, the Core funds will already own these stocks, and maybe willing to sell/buy to provide liquidity.
--this, incidentially, maybe why the simulated returns of the S&P 600 Value Index or Russell 2000 Value Index are 0.7% to 1.0% a year behind the simulated + live US Vector returns through Sept. despite much less factor risk from Vector. (the penality shows up in the index, and by default the index fund...its not as apparent looking at index fund v. index)

c) I do think, over a normal asset cycle, there does exist the need for consistent rebalancing between TSM and SV if your goal is to target a constant risk profile. Less so for TSM and LV, or LV and SV. Also not as big an issue if large, periodic contributions are available. Looking at the data over the last 30 to 40 years...with a 20% mandate, we are looking at rebalancing at least every 2 to 2.5 years. If we isolate the last 10 years ended 2006, a TSM/SV portfolio that was designed to stay within +/- 20% bounds had to be rebalanced 7 times. As a matter of fact, I found that the tax cost for rebalancing almost completely consumed any diversification bonus on a given portfolio over time (0.25% to 0.4% a year). This isn't as much of an issue with Core portfolios that have a small value/small component addition, and with Vector, its completely unnecessary.

All in all, you can achieve reasonable risk factor exposure (as you've shown) with ETFs and BRSIX in the US. Its getting easier in the overseas markets (although I don't think a 0.4HmL or more with a size tilt will be possible anytime soon) as long as you are willing to adopt exclusively value and small indexes. Once the MSCI EM Value Index hits, you will also need 100% of that for EM exposure to get a "moderate" HmL tilt.

I prefer the consistent global tilt because of the diversification efficiencies. If we go back to 1981 (US and Int'l factor premiums are as similar as I can find -- and I assume premiums to be close in the future), the difference between a 50/50 US/Int'l portfolio that takes equal size/value risk in the US and overseas has about 1% higher risk adjusted returns vs. a portfolio that takes all the size/value risk in the US, and sticks with EAFE for overseas exposure.

I believe the tilt is what matters, DFA just makes it a bit more efficient and seamless across regions.

SH

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Re: Previous realized losses

Post by Kenster1 » Sat Oct 13, 2007 9:32 am

grabiner wrote: None of the funds realized capital gains, so what you are seeing is the effect of the dividend yield. The Bridgeway ultra-small company market funds has the lowest dividend yield, partly because it has the highest expenses of any of the indexes, and partly because micro-caps are less likely to pay dividends.

Bridgeway's fund is tax-managed and may be able to avoid realizing gains, but I wouldn't expect small-value funds to be able to avoid gains forever. The small-cap value index realized a lot of losses in 2000-2002 and has been able to offset its gains with those losses.

And actually, the lowest tax cost of all is DFA Emerging Markets Index, with Vanguard second (and probably only second because it has lower costs and thus more taxable dividends). The foreign tax credit is worth about 0.24%, and you lose it in a tax-deferred account, so the DFA index actually has a tax cost of zero (equal returns in taxable and tax-deferred!) and Vanguard's is 0.09%.
Grabiner -- I'm not sure what you mean with respect to SCV which I highlighted in bold.

What is meant by realized a lot of losses in 2000-2002? The only loss was a 12-14% loss in 2002 depending on the index. Vanguard's SCV had a 14% loss in 2002 but other than that, it had double-digit gains in 2000, 2001 and then subsequently in 2003.
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Post by SmallHi » Sat Oct 13, 2007 9:48 am

I think its unrealistic to assume, longer term, any SV investments will remain extremely tax efficient and capture the SV premium. DFA is a bit more skillful in the latter, ETFs in the former

I think the only way to avoid the costly taxes and trading consequences of selling appreciated SV stocks will be to not sell them at all...allow them to become part of your mid/large cap allocation.

SH

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Re: Previous realized losses

Post by grabiner » Sat Oct 13, 2007 11:55 pm

Kenster1 wrote:
grabiner wrote: Bridgeway's fund is tax-managed and may be able to avoid realizing gains, but I wouldn't expect small-value funds to be able to avoid gains forever. The small-cap value index realized a lot of losses in 2000-2002 and has been able to offset its gains with those losses.
Grabiner -- I'm not sure what you mean with respect to SCV which I highlighted in bold.

What is meant by realized a lot of losses in 2000-2002? The only loss was a 12-14% loss in 2002 depending on the index. Vanguard's SCV had a 14% loss in 2002 but other than that, it had double-digit gains in 2000, 2001 and then subsequently in 2003.
The 2000-2002 losses are corect for most funds, and I am used to writing them when I refer to the bear market, but they are incorrect for this fund.

However, Small-Cap Value Index did lose a lot more than the year-start-to-year-end loss from its 2002 peak to its 2003 bottom, and its share value lost even more because of dividend payouts. The share price dropped from 11.66 to 7.66, a 38% decline, which led to a lot of capital losses being realized, particularly since the fund tracked a higher-turnover index at the time. Its last capital-gains distribution was in March 2002, just before that peak, so it started realizing losses in 2002 and hasn't used them up yet.

It currently has 2.5% in realized losses, and I would expect that to last only one more year; if the bull market continues, a gain distribution in 2008 is likely.

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Post by Robert T » Sun Oct 14, 2007 8:26 pm

.
SH,

Thanks for the thoughtful response. Here are some additional thoughts on each of the points:

a) on drift in risk factor exposure

Annual ‘style’ drift is more significant in indexes with annual reconstitutions (eg. the Russell indexes) than those with more continuous changes e.g. S&P indexes (the 600 series made additions/deletions at least monthly/almost weekly according the actual data over the past year). ‘Some’ style drift may not negatively impact returns due to momentum effects – similar to the potential for a ‘rebalancing’ bonus (or more accurately - a delayed 'rebalancing' bonus) at the portfolio level (using rebalancing bands). But I understand the desirability of more constant risk exposure.

b) on market impact

I agree market impact shows up in an index, but again is more extreme in some indexes such as the Russell indexes (transparent formula based approach to security inclusion with annual reconstitution that causes significant reconstitution arbitrage) versus the S&P indexes (with a committee based approach guided by a general formula with reconstitution on an as needed basis). Swensen has an excellent section in his book on these differences. The two points above are reason I prefer S&P indexes over Russell indexes.

Similarly this effect maybe more significant in ETFs with more extreme tilts – but a small-netural-value portfolio already captures much/most of the ‘migration’ benefits of small value integration in the core approach. As we know from the Fama-French Migration analysis most of the migration from small value has been to small ‘neutral’ (16% by mkt cap with about 70% staying put), while only 8 percent moved to large cap value or ‘neutral’. And most of the migration from small ‘netural’ was to small value (also 16% with about 60% staying put, 9% to small growth, and 8% to large cap value or ‘neutral). Following the numbers from the FF paper, and assuming this migration pattern continues, one could argue that a small-neutral-value (SNV) fund captures about two-thirds of the ‘migration’ benefit of integrating small value into a core portfolio (assumes migration to large and small cap growth are sold in both the small-neutral-value portfolio and a core type portfolio). In this respect I currently prefer ishares 600 value to ishares 600 pure value.
--this, incidentially, maybe why the simulated returns of the S&P 600 Value Index or Russell 2000 Value Index are 0.7% to 1.0% a year behind the simulated + live US Vector returns through Sept. despite much less factor risk from Vector. (the penality shows up in the index, and by default the index fund...its not as apparent looking at index fund v. index)
In an earlier post – I also thought that reconstitution arbitrage shows up as negative alpha in 3F regressions (as in the large negative alpha for the Russell 2000v index) which leads to lower returns than the factor loadings suggest. However if this effect is already reflected in the index – and the index itself is used to determine risk exposure (loadings) I am not sure this is the source of the difference – it may lie elsewhere (beta, or standard errors?). I don’t recall getting such a wide difference between actual ishares600v returns and that suggested from the Fama-French factor returns data (multiplied by the estimated factor loadings) – but will recheck.

c) on rebalancing (within US, non-US developed, and EM)

I agree that one fund can eliminate the need for rebalancing within the US, Non-US and EM segments. In early accumulation, component rebalancing can be done with new savings, however as portfolio size grows and the rebalancing needs exceed what new flows/savings can provide then the core approach reduces the costs of rebalancing by sale and purchase. However if the core funds rebalance daily then the ‘momentum’ effect better captured in broader rebalancing bands used in a component portfolio may off-set the additional costs of rebalancing. [Doesn’t DFA use momentum screens in the core funds?].

d) on exposure to risk factors in overseas markets

I agree that options to tilt to small and value in non-US markets are fairly limited (relative to the US). And if we want zero (not negative alpha) value funds – then the RAFI non-US indexes are among the options. I would also prefer a more consistent global value tilt but the last time I looked at this the return difference between an even value loading across the US and non-US and what I currently target was 0.2% (from an earlier post).

If I make any portfolio changes in the future it will likely be to try to get a more even risk factor split. And if DFA had TA vector funds for the US, Non-US developed, and EM I would seriously consider them. Although by having a higher size loading I may have to live with shortening my term exposure from 0.5 to about 0.2 to get a similar portfolio expected return...:)

Robert
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Post by SmallHi » Mon Oct 15, 2007 12:50 pm

I also thought that reconstitution arbitrage shows up as negative alpha in 3F regressions (as in the large negative alpha for the Russell 2000v index) which leads to lower returns than the factor loadings suggest. However if this effect is already reflected in the index – and the index itself is used to determine risk exposure (loadings) I am not sure this is the source of the difference – it may lie elsewhere (beta, or standard errors?). I don’t recall getting such a wide difference between actual ishares600v returns and that suggested from the Fama-French factor returns data (multiplied by the estimated factor loadings) – but will recheck.
(I may have misunderstood your comment here, but my comment is:)

Actually, this index constitution bias is reflected in the returns of the Index/fund (such as Russell 2000 or S&P 600), but not the Benchmark factors used to calculate the 3F risk premiums -- the Fama French series.

The Citigroup Small Value series had a negative alpha of 0.16% per month. That was lower than the Russell 2000 Value (-.25%/month), and in line with the MSCI 1750 Small Value index. I hesitate to make too much of any of this, as only the r2K VL index had statistically significant negative alpha.
However if the core funds rebalance daily then the ‘momentum’ effect better captured in broader rebalancing bands used in a component portfolio may off-set the additional costs of rebalancing. [Doesn’t DFA use momentum screens in the core funds?].
Core's rebalance daily with new portfolio dollars. So, if there is $10M per day coming into US Core 2, that money theoretically will be used only to buy stocks in categories that have experienced migration (and contain less than ideal #/% of holdings).

I would imagine the momentum effect would be even larger in Cores because those migrating SV stocks maynot be sold until they become much, much bigger Large or Growth stocks....The newer, larger capitalization of the recently migrated company is accounted for by the fact that w/i TSM, it now commands a larger weighting in the portfolio, and in Small and Mid Cap and Value segments, Cores have a higher target % of that stock than TSM does...money may even have to be added to these stocks to account for market cap targets than can be as much as 3 to 5 times the TSM allocation -- but I have no idea if this actually happens. At the very least, I cannot imaging they are sold at all (which is why I say they are even more "momentum friendly").

In component funds/ETFs such as iShares or DFA, even with "buffer zones", micro and small value stocks must be sold completely by the time they reach "mid cap" or "blend" ranges. Their larger market caps and price/book values risk contaminating the lower cap and p/b targets of strict S/V funds -- but will be held almost in their entirety? within the Core structure.
I would also prefer a more consistent global value tilt but the last time I looked at this the return difference between an even value loading across the US and non-US and what I currently target was 0.2%
Boy, this is hard to quantify! I read that post you linked, even made a quick comment on it (I see :D ) My opinion would be that a consistent global small/value tilt maybe worth a bit more than 0.2%, but cannot be sure.

I am more used to modeling this stuff using the actual Fama/French Index series along with S&P 500 and EAFE for market exposure. I found, going back to 1975 (thru 2006), a US/Int'l portfolio that is 50% market, 25% LV, and 25% Small" both in the US and EAFE markets (P1)had 0.9% a year higher risk adjusted returns vs. a US/Int'l portfolio that was split evenly between US LV and US Small for domestic, but 100% EAFE Market for foreign (P2).

The above example suffers from the fact that S&P had higher returns than EAFE for the period under question, and annualized MkT-LV and MkT-Small premiums were higher internationally than in the US.

The best I can do to remedy this is to observe the 1975-1999 period, where US LV and US Small annualized returns were almost identical to Int'l LV and Int'l Small results (but EAFE still trailed S&P by over 2% a year). During this period, P1 outpaced the risk adjusted return of P2 by about 1.2% annually.

(I made these portfolios risk neutral by adding 5% 1YR T-Notes to P2 in each example to make standard deviation identical)

Suffice it to say, different approaches to looking at the Global Factor allocation decision will reasonably come up with different measures of value. How much EM S/V adds to this is another discussion for another day.
And if DFA had TA vector funds for the US, Non-US developed, and EM I would seriously consider them. Although by having a higher size loading I may have to live with shortening my term exposure from 0.5 to about 0.2 to get a similar portfolio expected return...
Yikes, I cannot imagine you hiring an advisor for DFA access...and based on what you have written here the last few months -- that would seem about the only reason for you to do it. I am of the opinion that you are smarter than the average "low cost-advisor" you would likely be looking to for DFA access, the exception of course being Equius's new low cost venture.

As for your above-proposed fixed income decision, I have to hand it to you Robert, you are a lot more precise than I am! :D

I am too lazy to even consider why that would be the case :shock:

Keep up the great research, they are great bookmarks to go back to from time to time. I wish there were a better place to discuss almost exclusively Multifactor Investing -- a place that doesn't get bogged down in DFA vs. Vanguard vs. iShare debates.

SH

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Post by Robert T » Tue Oct 16, 2007 6:37 am

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SH

Do reconstitution effects impact alpha?

I seem to get similar alpha results to you. Here are the estimated alphas for three value indexes and the DFA small value fund (using monthly data from July 1995 to April 2007). All indexes have negative alpha – lowest for the DFA fund, similar for the MSCI and S&P fund and highest for the Russell 200v (the only significant alpha).

Code: Select all

July 1995-April 2007
                                        Alpha     t-stat  
MSCI US Small Value Index               -0.18     -1.48
S&P 600 Value                           -0.19     -1.49
Russell 2000 Value                      -0.26     -2.40
DFA Small Value                         -0.13     -1.25
(from earlier post http://www.diehards.org/forum/viewtopic ... ght=#33735)

I am not sure that this is a reconstitution effect (although the relative magnitudes are consistent with the expected effect based on portfolio construction). If reconstitution arbitrage bids up the price of securities before they enter the index and lowers the prices of those that exist this should show up as slightly lower value loadings (due to higher prices of stocks entering) and lower size loadings (also do to the higher prices) than if arbitrage did not take place. So my sense is that it also show-up in factor loading (perhaps some of the effect also makes it through to alpha. Here were my earlier thoughts on the negative alpha’s (from an earlier post).

Negative alpha on value funds: The negative alpha is not unique to the S&P Pure Value index but seems common across most value indexes (see table below). Arnott highlighted this in his ‘Fundamental Indexation’ paper “…most value indexes earn an estimated Fama–French alpha of –1.5 percent or worse” (presumably per year). The negative alphas are difficult to fully interpret. The easy route is just to say they are statistically not significantly different from zero (which is often the case, except for the alpha on the Russell 2000 value index) so no need to worry. Bernstein suggests its just a flaw in the model “the alphas of these indexes, which are statistically significant, represent a flaw in the model, which does an otherwise excellent, but obviously not perfect, job of predicting an extraordinarily complex system using just three variables. The Three-Factor Model is, as Fama and French have repeatedly emphasized, only a model — it is not reality.” Arnott attributes the negative alpha to poor construction of the indexes. Perhaps there is some truth to both these views. For example the significant negative alpha on the Russell 2000 value index maybe capturing the effects of the reconstitution arbitrage which seems widely acknowledged (see for example Swensen’s Unconventional Success pg. 251-257 on the Russell index construction). IMO other indexes being tracked by mutual funds may also not be immune to this effect.

Momentum

Larry’s recent link to new analysis on momentum indicates that the entire effect is in just 4% of the market and in only the high credit risk companies. So the effect seems more dominant in small and value companies. I am not sure which is larger – positive or negative momentum and the net effect on a core type strategy vs. component approach.

Measuring the global factor diversification effect

I agree it is difficult to do accurately (and is always backward looking). I preferred to use the Fama-French Intl HmL factor in the earlier analysis for consistency, as this is what I used to estimate my international value loadings and to construct a FF factor benchmark. Who knows what the difference will be going forward? But if we follow Sinequefield’s view then the expected factor return across US and Non-US developed markets are the same (although you don’t get the diversification effect). “Asset pricing models, other than segregated models, do not argue that risk factors have geographically different expected returns.” http://www.cfapubs.org/doi/pdf/10.2469/faj.v52.n1.1961

Non-linearity in factor returns

The soon to be publiched JoF article by Fama-French http://www.afajof.org/journal/forth_abs ... sp?ref=429 highlights non-linearity in the size premium. “The regressions say that the size effect (the original center-stage anomaly) owes much of its power to microcaps and is marginal among small and big stocks.” The non-linearity effects seems less extreme (more linear) in value stocks.

Current approach

I am currently sticking with my plan – get US value exposure with small and mid-caps (using S&P indexes – lower turnover, market impact, REITs, dividend yield, and taxes than available alternatives), get US size exposure with micro caps (using Bridgeway fund that targets CRSP10 – as I prefer a more focused approach to managing transaction costs in micro-cap stocks than is the case with some micro-cap ETFs [as I understand them]), and get overall US market exposure through Vanguard’s low cost TSM. On the international side, I agree choices are more limited – but will currently stick with EAFE value for value exposure (although the negative size loading and low value loading is not great). On DFA – I will certainly monitor performance of their core/vector funds and am still sticking by Bernstein’s guide – what matters over the long-term is factor exposure and expense, which will guide any security selection changes in the future.

Robert
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Post by SmallHi » Tue Oct 16, 2007 10:03 am

Robert,

Thanks for the thoughtful post. Interesting that Eduardo Repetta and Fama/French seem to disagree on the linearity of the size premium. FF saying there is a micro cap bulge, Repetta (in a recent Index Universe article) claiming there is a "linear gradation between returns and sizes of companies".

As I am sure you are aware, the real world evidence differs depending on which period you observe. The 1927-1966 period shows almost the entire size premium existing in CRSP 9-10. The 1967-2006 period shows you get all of the size premium out of CRSP 6-8, and the vast majority of it from CRSP 3-5.

About the only constant is, there is a significant negative size premium in CRSP 1. It appears you can pick up at least some "size exposure/return premium" in your portfolio by simply avoiding the biggest mega-cap stocks in the market. They have historically underperformed an equal weighted portfolio of CRSP 2-10 by about 2.8% a year. The actual size premium as computed by FF (6-10 minus 1-5) has only annualized at 2.3%

As I understand it, the Core portfolios attempt to capture the size premium in varying degrees as much by underweighting mega cap stocks as they do overweighting medium, small, and micro names.

The mega/micro vs. medium/small debate may never end!

SH

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Post by larryswedroe » Tue Oct 16, 2007 12:28 pm

Robert
The only momentum effect is NEGATIVE and only in that tiny segment of the market--and way to play it is to avoid the negative effects of buying negative momentum stocks as they enter the buy zone for a passive asset class fund--an index fund would buy it.

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Momentum

Post by Robert T » Tue Oct 16, 2007 5:09 pm

.
Thanks Larry,

I did not know that. I thought there was both positive and negative momentum in both individual stocks and asset classes (signficant autocorrelation of past returns on current returns during periods of both positive and negative returns and more signifcant for shorter periods than longer periods). I will read the earlier linked article again...

Robert
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Post by SmallHi » Wed Oct 17, 2007 11:52 am

Larry,

I cannot say with any certainty that you are wrong, but, I do know that whle at U of Chicago, Cliff Asness did a lot of work studying momentum under Fama within individual securities, and I believe he found momentum both ways -- ups tend to continue to go up, and downs continue to go down, at least for a month or two.

While he runs a lot of different hedge strategies today, it is my understanding that one of the core themes he still uses is a long/short HmL strategy (short the negative momentum, low BtM stocks and buy positive momentum, high BtM stocks with the proceeds).

I am certainly not advocating such an approach (at last check, going long DFAs US Large Value and Small Value funds (or US Vector) and dampening risk w/5YR Global was more efficient and had done better anyway), but, I doubt he would undertake such a process if in fact he found momentum was only negative and in a small corner of the market.

Just thinking out loud here...

SH

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Post by larryswedroe » Wed Oct 17, 2007 7:47 pm

SH

Yes there is positive momentum and DFA has always benefitted from it via the hold ranges, but the costs of exploiting it if have to buy the stocks exceeds the benefits--at least to my knowledge

Same thing on the negative side--

The way it works is that you can at best avoid the pernicious negative effect of negative momentum and can gain the good effects if do what DFA does.

Again, that is to my knowledge

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